Semi-implicit complementary volume scheme for solving level set like equations in image processing and curve evolution

Summary. We introduce linear semi-implicit complementary volume numerical scheme for solving level set like nonlinear degenerate diffusion equations arising in image processing and curve evolution problems. We study discretization of image selective smoothing equation of mean curvature flow type given by Alvarez, Lions and Morel ([3]). Solution of the level set equation of Osher and Sethian ([26], \[30]) is also included in the study. We prove and estimates for the proposed scheme and give existence of its (generalized) solution in every discrete time-scale step. Efficiency of the scheme is given by its linearity and stability. Preconditioned iterative solvers are used for computing arising linear systems. We present computational results related to image processing and plane curve evolution. Received April 25, 2000 / Revised version received June 11, 2001 / Published online November 15, 2001     

Ambient connections realising conformal Tractor holonomy

For a conformal manifold we introduce the notion of an ambient connection, an affine connection on an ambient manifold of the conformal manifold, possibly with torsion, and with conditions relating it to the conformal structure. The purpose of this construction is to realise the normal conformal Tractor holonomy as affine holonomy of such a connection. We give an example of an ambient connection for which this is the case, and which is torsion free if we start the construction with a C-space, and in addition Ricci-flat if we start with an Einstein manifold. Thus, for a C-space this example leads to an ambient metric in the weaker sense of Čap and Gover, and for an Einstein space to a Ricci-flat ambient metric in the sense of Fefferman and Graham. Current address for first author: Erwin Schr?dinger International Institute for Mathematical Physics (ESI), Boltzmanngasse 9, 1090 Vienna, Austria Current address for second author: Department of Mathematics, University of Hamburg, Bundesstra?e 55, 20146 Hamburg, Germany     

Nondispersive two-electron wave packets in driven helium

We provide a detailed quantum treatment of the spectral characteristics and of the dynamics of nondispersive two-electron wave packets along the periodically driven, collinear frozen planet configuration of helium. These highly correlated, long-lived wave packets arise as a quantum manifestation of regular islands in a mixed classical phase space, which are induced by nonlinear resonances between the external driving and the unperturbed dynamics of the frozen-planet configuration. Particular emphasis is given to the dependence of the ionization rates of the wave packet states on the driving field parameters and on the quantum mechanical phase space resolution, preceded by a comparison of 1D and 3D life times of the unperturbed frozen planet. Furthermore, we study the effect of a superimposed static electric field component, which, on the grounds of classical considerations, is expected to stabilize the real 3D dynamics against large (and possibly ionizing) deviations from collinearity. Received 7 November 2002 / Received in final form 2 December 2002 Published online 28 January 2003     

Thermal conductance for single wall carbon nanotubes

We report a theoretical analysis of the phonon thermal conductance, κ(T), for single wall carbon nanotubes (SWCN). In a range of low temperatues up to 100 K, κ(T) of perfect SWCN is found to increase with temperature, approximately, in a parabolic fashion. This is qualitatively consistent with recent experimental measurements where the tube-tube interactions are negligibly weak. When the carbon-carbon bond length is slightly varied, κ(T) is found to be qualitatively unaltered which implies that the anharmonic effect does not change the qualitative behavior of κ(T). Received 12 June 2001     

Series solution to the laser-ion interaction in a Raman-type configuration

The Raman interaction of a ultracold ion trapped with two travelling wave lasers is studied analytically with series solutions, in the absence of the rotating wave approximation (RWA) and without restrictions of both the Lamb-Dicke limit and the weak excitation regime. The comparison is made between our solutions and those obtained under the RWA in order to demonstrate the validity region of the RWA. As a practical example, the preparation of Schr?dinger-cat states is proposed beyond the weak excitation regime, using our calculations. Received 12 March 2001 and Received in final form 16 October 2001     

Molecular flow and wall collision age distributions

The use of storage cells has become a standard technique for internal gas targets in conjunction with high energy storage rings. In case of spin-polarized hydrogen and deuterium gas targets the interaction of the injected atoms with the walls of the storage cell can lead to depolarization and recombination. Thus the number of wall collisions of the atoms in the target gas is important for modeling the processes of spin relaxation and recombination. It is shown in this article that the diffusion process of rarefied gases in long tubes or storage cells can be described with the help of the one-dimensional diffusion equation. Mathematical methods are presented that allow one to calculate collision age distributions (CAD) and their moments analytically. These methods provide a better understanding of the different aspects of diffusion than Monte Carlo calculations. Additionally it is shown that measurements of the atomic density or polarization of a gas sample taken from the center of the tube allow one to determine the possible range of the corresponding density weighted average values along the tube. The calculations are applied to the storage cell geometry of the HERMES internal polarized hydrogen and deuterium gas target. Received 9 July 2001 and Received in final form 18 September 2001     

Completely empty pyramids on integer lattices and two-dimensional faces of multidimensional continued fractions

In this paper we develop an integer-affine classification of three-dimensional multistory, completely empty convex marked pyramids. We apply it to obtain the complete lists of compact two-dimensional faces of multidimensional continued fractions lying in planes at integer distances 2, 3, 4, …  to the origin. The faces are considered up to the action of the group of integer-linear transformations.     

Fabrication of bamboo-shaped GaN nanorods

Bamboo-shaped GaN nanorods were formed through a simple sublimation method. They were characterized by means of X-ray powder diffraction (XRD), transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM) and selected-area electron diffraction (SAED). The TEM image showed that the nanorods were bamboo-like. XRD, HRTEM and SAED patterns indicated that the nanorods were single-crystal wurtzite GaN. Received: 8 January 2001 / Accepted: 28 April 2001 / Published online: 20 December 2001     

Scale-free behavior of the Internet global performance

Measurements and data analysis have proved very effective in the study of the Internet's physical fabric and have shown heterogeneities and statistical fluctuations extending over several orders of magnitude. Here we focus on the relationship between the Round-Trip-Time (RTT) and the geographical distance. We define dimensionless variables that contain information on the quality of Internet connections finding that their probability distributions are characterized by a slow power-law decay signalling the presence of scale-free features. These results point out the extreme heterogeneity of Internet delay since the transmission speed between different points of the network exhibits very large fluctuations. The associated scaling exponents appear to have fairly stable values in different data sets and thus define an invariant characteristic of the Internet that might be used in the future as a benchmark of the overall state of “health” of the Internet. Received 25 January 2003 Published online 7 May 2003